GRB's are so bright they are detectable throughout the observable universe. They have been detected at redshifts in excess of z = 9. Supernova, by comparison, are only detectable up to about z = 2. The beaming idea is just one possible explanation among several.

They do have to be aimed at us for us to see them. The answer to your question gives a feeling for just how large the universe is. Supernovae go off at the rate of about 1 per galaxy per 100 years. Since there are about 10^11 galaxies in the observable universe, that means there are about 100,000 supernovae per day in the observable universe. We think only about 1 in 1000 of these have the right conditions to produce a GRB, and only about 1 in 100 of these are aimed at us, so we see about one per day. These are very rough numbers, but you get the idea.

okay, that's what I thought. I just wanted to make sure I had the right idea about how "common" they are. I put common in quotes because I guess they're only really common when we're talking about the whole observable universe.

okay, that's what I thought. I just wanted to make sure I had the right idea about how "common" they are. I put common in quotes because I guess they're only really common when we're talking about the whole observable universe.

Also these sorts of rough guesses are good examples of why "beaming" makes sense. You can do rough numbers about how many GRB we expect to see, and they are more or less how many we do see.

shouldn't the number of bursts that miss us be a lot larger than the number that miss us? more than 1 to 100, I mean.

Unless the beams of gamma rays are very "wide", then shouldn't it be really easy for them to miss us? Or is it that the beam spreads out over long distances, similar to how lasers spread out?

I would imagine that the beam would only be as wide as a large star, since that's what forms them (according to the theory), right? So unless it spreads out as it travels, then it should be really easy to miss us, and thus the number of them that hit us should be very very very small.

This paper gives the distribution of opening angles in Figure 3. The opening angle is typically about 10 degrees. It is a fixed angle, so of course the beam spreads as you get further away. We can calculate the probability of being in the beam as follows: If the beam has an opening angle of 10 degrees (1/6 radian), this is a half-angle of 5 degrees (1/12 radian). So the solid angle of one beam is about pi*(1/12^2) steradians. Since there are two beams, and 4*pi steradians in the sphere, the probability of a given point being in the beam is about

P = (2*pi/144)/(4*pi) = 1/288

So maybe my 1/100 chance of being in the beam should have been 1/300, but I was just giving rough order of magnitude numbers, since there are many uncertainties.